# What is the equation of the line tangent to #f(x)= -(3-2x)^2 # at #x=-2#?

y - 28-x - 7 = 0

To obtain the equation of the tangent , y-b = m(x-a) , we

require to find the gradient , m , and the point ( a,b).

f'(x) is the gradient of the tangent and f'(-2) will give it's

value. The x-coord is given, x = -2 and to find b , the y-coord

evaluate f(-2).

and f'(-2) = 4(3+4) = 28 = m

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The equation of the line tangent to f(x) = -(3-2x)^2 at x = -2 is y = -16x - 25.

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